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Very roughly, universal algebra is the study of those classes of algebraic structures which can be defined via a set of equations; such a class is called a variety. Of course there is far more to the ...

Welcome to my first MathOverflow posting! This is a question about rings, all of them assumed to be both unital and associative. Let $f\colon R\to S$ be a map between rings such that $f(xy)=f(x)f(y)$ ...

Consider a Cayley-Dickson algebra $(X,+,∗,0,1)$, that is an algebra generated from the reals by the Cayley-Dickson construction. From complexes to quaternions, we lose commutativity of multiplication, ...

In Gödel logic, is conjunction definable from implication, negation , and disjunction? We know that conjunction in that logic is not definable from negation and implication.

Let $\mathfrak{A}=(A;...)$ be an algebra in the sense of universal algebra. Say that a congruence $\sim$ on $\mathfrak{A}$ is parafinite iff there is an equivalence relation $E\subseteq A^2$ with ...